Problem: What do the following two equations represent? $x+4y = -2$ $3x+12y = -1$
Answer: Putting the first equation in $y = mx + b$ form gives: $x+4y = -2$ $4y = -x-2$ $y = -\dfrac{1}{4}x - \dfrac{1}{2}$ Putting the second equation in $y = mx + b$ form gives: $3x+12y = -1$ $12y = -3x-1$ $y = -\dfrac{1}{4}x - \dfrac{1}{12}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.